GLENAVON grabbed the lead on 22 minutes through Jay Magee whose effort from a Conor Hagan free-kick took a big deflection through a crowded penalty area on its way past Niall Morgan.
Niall Henderson came closest to doubling Glenavon's advantage five minutes into the second half when smashed the ball off the underside of the bar from just inside the area.
Diarmuid O'Carroll came close to doubling Glenavon's lead on 80 minutes only to send an effort just wide.
But Dungannon stormed back to snatch a share of the spoils two minutes into stoppage time when, from a Shea McGerrigan corner, Dermot McCaffrey tapped the ball home at the back post.
Glenavon: O'Hare, Shannon, Neill, Jay Magee, Henderson, O'Carroll, Miskimmin, Hagan, Doherty, Turkington, Graham subs Harpur (replaced Henderson 88), Kelbie (replaced Miskimmin 86), D. Magee (replaced Graham 72), Davidson (not used), McGonnell (not used)
Dungannon Swifts: Morgan, McCluskey, Montgomery, McCaffrey, McClean, Funston, Fitzpatrick, Topley, P.J. Lavery, S. Lavery, Ward subs McMinn (not used), McCready (replaced MCClean 78), Murphy (not used), McGerrigan (replaced P.J. Lavery 78), McKerr (replaced Funston 69)
- Swifts players celebrate Dermot McCaffrey's late equaliser (Picture: Gareth Irvine/PressEye.com)